Question: Rewrite as a simplified fraction. ${1.3\overline{39} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1339.3939...\\ 10x &= 13.3939...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1326}$ ${x = \dfrac{1326}{990}} $ ${x = \dfrac{221}{165}} \text{or} {1 \dfrac{56}{165}}$